From Relays to Transistors.

In this lecture we meet for the first time electronic devices that
can increase the power of a signal. The most common device
that can achieve this is the transistor.
However we have already met relays, in which you will recall
the input current is passed through a coil
thereby generating a magnetic field which then operates a conventional
mechanical switch. A relay can convert a low power signal (perhaps 5 volts
at 10mA, so 0.05 watts) to a high power signal (perhaps 1A at 10V, so 10
watts).
However, while relays have the desirable property that the input is
electrically isolated from the output, they have many drawbacks.

They are essentially digital - the contacts are either open or closed,
with no intermediate state.

They have a short life-time - perhaps a few million operations. A
transistor can operate many millions of times per second for
years.

Transistors are electronic devices which avoid all these pitfalls. However
they do not provide electrical isolation between input and output.
Isolation is typically provided opto-electronically, in which the signal
is converted to and from light.

Transistors provide electronic amplification

Transistors are "active" components which can increase the
power of a signal. Don't confuse voltage gain with power gain - a step-up
transformer gives voltage gain, but no power gain, since current is reduced
proportional to the step up in voltage.

There are two basic kinds of transistor, the bipolar transistor
and the field effect transistor. These differ significantly in their
characteristics. In this course we will use bipolar transistors for our
construction, but we shall discuss the properties of field effect transistors
because they occur in many components that we need to interface to. Integrated
circuits are arrays of transistors and other components formed on a single
chip of semiconductor material. Most of the latest chips use field effect
transistors (making them the most common kind of transistor in terms of
numbers - there are millions in a modern chip), but in many cases interface
standards are determined by the requirement for compatibility with the
bipolar technology which on which earlier integrated circuits were based.

Transistors are semiconductor devices

Metals are conductors of electricity because they have many conduction
electrons which are not attached to any particular atom. In an insulator,
each electron is firmly attached to atoms in its locality. A semiconductor
can be thought of as a (rather bad) insulator which is made to be conductive
primarily by the presence of impurities.

The role of these impurities can be understood in terms of the chemical
concept of valence. Atoms are formed into molecules of a
chemical substance by being attached through chemical bonds.
Early chemists observed that a given kind of atom, that is to say an atom
of a given chemical element, preferred to form a number of bonds that
was characteristic of that element. Hydrogen atoms for example like to
form one bond, while oxygen atoms like to form two. Consequently when
hydrogen and oxygen combine to form water, they do so in the proportion of
two hydrogen atoms to every one oxygen atom - we can draw a picture like
this:

H - O - H

giving the well known formula H2O.

This
preference of an atom for forming a given number of bonds is known as
valence. Hydrogen is said to be monovalent while oxygen
is said to be bivalent.

The concept of valence doesn't explain all chemical phenomena.
For example, according to the above rules the substances

H - O - O - H
H - O - O - O - H
.....

should exist. Indeed the first of these does exist, it's the substance
familiar to those who desire a blondness of hair with which nature has
not gifted them, hydrogen peroxide. But it's very much less stable than
water (which is why it works as a bleach). In fact long chains of oxygen
atoms bonded together are just not stable.

However when we come to tetravalent atoms like carbon and
silicon we find that we can get very stable structures in which, say,
silicon atoms are bonded to each other. Thus silicon can form a crystal,
which is in effect a giant molecule in which every silicon atom is bonded
to four neighbours in a regular array which extends for millions of atoms
in each direction.

Originally chemical bonding was a quite mysterious process.
Atoms just liked to bond together to form molecules and that was
that. However gradually during the 19th century clues arose that somehow
electricity was involved in chemical bonding - for example some kinds of
bonds could be broken by passing an electric current. Eventually, in the
20th century, it was realised that chemical bonds are mediated by
electrons. Essentially, each chemical element has a characteristic
number of electrons (called the atomic number).

For example, silicon is a semiconductor
which is, chemically, tetravalent. If an atom of a pentavalent impurity
such as phosphorus is present in the lattice of a silicon crystal, its
extra valence electron is only loosely bound to it, and so is able to travel
in the crystal. Thus taking pure silicon and "doping" it with
a small proportion of a pentavalent impurity (we are speaking of parts-per-million)
makes it able to conduct electricity. This kind of doped silicon is called
an "N" type semiconductor, because electricity is carried through
it by these extra electrons, which are Negative.

A trivalent impurity gives rise to P-type silicon, which is also conductive
because the missing valence electrons gives rise to ``positive holes'',
which can be thought of as mobile carriers of positive charge.

A silicon diode is formed as a junction of a piece P-type silicon and
a piece of N-type silicon. To each of these is bonded a metal lead, being
the terminals of the diode. If the negative terminal of a power supply
is connected to the P-type silicon and the positive terminal to the N-type
silicon, then the respective carriers are drawn away from the junction,
and hence no current passes. We say that the material immediately around
the junction forms a depletion region, where there are few carriers. If
the polarity of the connection is reversed, electrons and holes are driven
in opposite directions through the junction, and current flows.

A bipolar transistor is a 3 terminal device. The 3 terminals are called
the emitter, the base, and the collector. Such transistors come in two
flavours. A NPN transistor has the emitter and the collector made of N-type
silicon, while the base is made of P type silicon. A PNP transistor is
the opposite "sandwich".

NPN transistors have superior high frequency properties, and are the
default kind of transistor to use. PNP transistors can be used to provide
neat solutions to circuit design problems. For example, a ``complementary
pair" of NPN and PNP transistors is often used to create an efficient
circuit for driving a loudspeaker.

For an NPN transistor to operate correctly the following rules
(drawn from Horowitz and Hill) apply:

the collector must be more positive than the emitter.

The base-emitter and the base collector circuits behave like diodes.
Normally, the base-emitter diode is conducting and the base-collector diode
is reverse-biased, i.e., the applied voltage is in the opposite direction
to easy current flow.

Any given transistor has maximum values of
IC, IB
and VCE which cannot be exceeded without knackering
it.

When
rules 1-3 are obeyed, IC is roughly proportional
to IB and can be written as

IC =hFEIB

Here hFE is called the current gain, and it is typically
about 100. Sometimes the Greek letter beta is used for the current
gain.

If the application of rule 4 would predict that the collector would
go more negative than the emitter because of the effect of circuit elements
elsewhere, then the transistor is said to be saturated.
Enough IC
current will flow through the transistor to keep the collector 0.05 to
0.2 volts more positive than the emitter. Typically the effective value
of hFE falls as the transistor approaches saturation.

Property 4 is the useful property of a transistor: A small current flowing
into the base controls a much larger current flowing into the collector.
The first 3 properties can usually be thought of as establishing pre-conditions
for property 4 to hold. Essentially, it says that the collector behaves
like a current source - a more refined model of a transistor shows that
it is a not-too-great current source.

The parameter hFE is poorly controlled in manufacture.
Thus, nominally identical transistors might have this parameter vary between
50 to 250. A circuit that depends on a particular value for hFE
is a bad circuit. You should design for the worst case - usually a
low value of hFE is problematic.

Do NOT put a voltage across the base-emitter terminals - you will fry
the transistor. You must always limit the current. Collector current is
NOT diode conduction - transistor action in an NPN transistor depends on
the P region being very thin. One way of thinking of the base is as a potential
hill which electrons find hard to cross. Putting P carriers into the depletion
region by biasing the base positively has the effect of flattening out
that hill. Surprisingly, most electrons then shoot straight across from
the emitter to the collector, although some fall by the wayside and ``recombine''
with P carriers. The extent of this recombination determines the current
gain of the transistor - the bigger the recombination the lower the gain.

Basic Transistor Circuits

The transistor switch

Where we have a switch, a 1k resistor in the base circuit of an NPN
transistor. There is a 10V power supply, with a 10V 0.1 amp lamp collector
load. The current gain is 100. So, there is a 9.4V drop across the resistor,
hence 9.4mA base current. So a collector current of 940mA? Well, no! Because
the lamp will drop 10V at 100mA! So the transistor is in saturation, with,
say, 9.8 volts across the lamp. The transistor is "over-driven"
into saturation - a good idea provided you don't exceed the maximum permissable
IB, since hFE effectively falls as
the transistor approaches saturation. A resistor to pull the base down
to ground is a good idea - it will reduce leakage in the off state. Notice
that the power dissipation of a transistor used as a switch is normally
quite low. When it is off, little current is flowing so P=IV is
small. When it is on, the voltage across the device is small, so again
P=IV is small. If a transistor is not in saturation the power
dissipation can be high, and a heat sink may be needed to avoid
knackering it.

The Darlington Connection

This behaves as a transistor whose current gain is the product of the
gains of the two transistors, and whose VBE is the sum
of the VBE's of the two transistors. The Darlington configuration
can be improved by the provision of a resistor from the base of Q2 to the
emitter of Q2. This means that the leakage current of Q1 does not bias
Q2 into conduction. It also allows Q1 to turn Q2 off faster. Darlington
transistors can be bought pre-packaged complete with the base-emitter resistor
included. We are using TIP106, which has a higher current gain than the
more common TIP120.

The Sziklai connection.

This uses a NPN transistor with the collector driving into the base
of a PNP transistor. It has only a single base-emitter drop, but always
has a diode-drop in saturation.

An example - operating track switches

We use packaged Darlington transistors for operating the track-switches
because of their high hFE. We can draw a current of about
2mA out of standard logic gates and will want several amps to drive a track-switch
motor (the resistance of the motor is 5 ohms, and its inductance will only
restrict the current it draws for a few milliseconds. So we need a current
gain exceeding 2500, which is offered by high-performance packaged Darlington
transistors.

Making Linear Amplifiers with Transistors

An amplifier is said to be linear if its output is proportional
to its input. If it is a linear (voltage)
amplifier then the relationship between input and output is

Vout = gVin+c

Here g is a constant called the gain of the
amplifier, while c is a constant called the offset.
The amplifier is called linear because the graph representing
the above equation is a straight line.
Naturally, there is a range of voltage over which an amplifier operates
linearly. Outside this range the amplifier typically becomes less sensitive
to changes in the input.
The figure shows the typical input-output behaviour of an
amplifier.

Linear Amplifiers

Linear amplifiers are important
whenever it is necessary to provide a precisely controlled electrical signal
to produce a particular desired effect. For example, for quality sound
reproduction, the current flowing through the coil of the loudspeaker(s)
involved must be proportional to the input voltage derived from
demodulating a radio signal or doing a digital-to-analog conversion of the
signal specified on a compact disc.
It is possible to build an amplifier completely out of discrete
transistors and
other components - resistors and capacitors are the most likely ones to be
employed. However today you will only do this because you want an
amplifier with very special properties. Cheap (less than 1$)
operational amplifiers are available as integrated circuits. We shall
discuss these in detail later. Most likely any amplifier you will build
will make use of operational amplifiers, but you may need to construct an
output stage out of power transistors , because the
run-of-the-mill operational amplifier typically only delivers at most 100ma
of output current - not enough to run most electric motors, for example.

Cascaded Amplifiers

Typically, an amplifier will contain several separate stages
each of which is based on a transistor. These stages are cascaded
so that the output of one stage drives the input of the next. The
gain of the whole amplifier is the product

[Note - gain is often measured in decibels, which are a logarithmic
measure so you add the gain in decibels.

There are 3 configurations of transistor that have been used in
constructing amplifiers, classified on the basis of which of the 3
terminals of a transistor is common to the input and output
circuits.

The common emitter circuit

This
combines both voltage gain and current gain, and is one of the basic
building blocks for amplifiers made out of discrete transistors. But, as I
have observed above, we don't often want to build such amplifiers any more.
A practical common-emitter amplifier-stage for AC amplification is shown in
the diagram. You will see that quite a complicated network of resistors is
required to determine the operating point , that is to say the
value of the output voltage when there is no input signal.

The common base circuit provides high voltage gain with a
current gain of slightly less than 1. It provides superior high-frequency
performance to the common-emitter circuit.

The Common Collector (or Emitter Follower)

The common collector circuit , or as it is usually known,
the emitter follower.

The emitter follower is the most useful transistor amplifier circuit
for general purpose use.

It has unit voltage gain, but a large current gain.
Why is it useful?
Because very cheap operational amplifiers are available which can be configured
to provide a big voltage gain. But they offer have limited output current.

A Push-Pull Output Stage

The diagram shows a useful way in which a NPN and PNP transistor
arranged as emitter followers can be used to drive a load, such as an
electric motor, that needs to be driven both forward and in reverse. You
can think of this circuit as being 2 halves, a top half and a bottom half.
If the input signal is positive with respect to ground, then the top half
of the circuit acts as an emitter follower, so that the voltage at the
motor is Vsignal - 0.6 (the VBE drop, approximately).
The lower transistor is turned off. Likewise if the input signal is
negative with respect to ground, then the voltage at the motor is
Vsignal + 0.6.
The next diagram is a graph relating the input signal to the output.
Essentially, the output voltage is proportional to the input except
for a region around the origin.

This circuit has quite a few virtues - it is simple, and it consumes zero
power when the input signal is zero. However the "glitch" at the origin is
undesirable. We shall see, when we consider operational amplifiers, how
this glitch can be almost entirely removed by the use of negative
feedback . However, we can also clean up the output significantly by
using diodes to cancel out the VBE drop, as shown in the next
circuit.